Distributed Real-Time Economic Dispatch in Smart Grids: A State-Based Potential Game Approach

The increased complexity of modern energy network raises the necessity of flexible and reliable methods for smart grid operation. To this end, this article is centered on the economic dispatch problem (EDP) in smart grids, which aims at scheduling generators to meet the total demand at the minimized cost. This article proposes a fully distributed algorithm to address the EDP over directed networks and takes into account communication delays and noisy gradient observations. In particular, the rescaling gradient technique is introduced in the algorithm design and the implementation of the distributed algorithm only resorts to row-stochastic weight matrices, which allows each generator to locally allocate the weights on the messages received from its in-neighbors. It is proved that the optimal dispatch can be achieved under the assumptions that the nonidentical constant communication delays inflicting on each link are uniformly bounded and the noises embroiled in gradient observation of every generator are bounded variance zero mean. Simulations are provided to validate and testify the effectiveness of the presented algorithm.

Event-triggered scheme for finite-time distributed economic dispatch in smart grids

This paper is dedicated to solving the economic dispatch problem in smart grids, which aims at minimizing the total generation cost while satisfying the power supply-demand balance and generation capacity constraints. A distributed algorithm is proposed to solve the economic dispatch problem over directed communication topologies that are time-varying unbalanced. Its features are that the proposed algorithm is push-based, and the model of line losses is integrated into the problem of our interest to reduce the power losses. Resorting to geometric graph theory and convex analysis, it is proved that the incremental costs achieve consensus at a convergence rate O(1 / √t ) with t being the number of iterations. Furthermore, robustness of the proposed algorithm is investigated solving the EDP when the communication information undergoes arbitrary large but bounded constant delays and the local gradients involve observation noises with zero-mean and bounded variance. Finally, three case studies implemented on an islanded microgrid, the IEEE 30-bus system and the IEEE 118-bus system are tested to demonstrate the effectiveness of the proposed algorithm.

The Economic Dispatch Problem (EDP) plays a critical role in power system operations by trying to allocate power generation across multiple units at minimal cost while satisfying complex operational constraints. Traditional optimization techniques struggle with the non-convexities introduced by factors such as valve-point effects, prohibited operating zones, and spinning reserve requirements. While metaheuristics methods have shown promise, they often suffer from convergence issues and constraint-handling limitations. In this study, we introduce a novel application of Group Relative Policy Optimization (GRPO), a reinforcement learning framework that extends Proximal Policy Optimization by integrating group-based learning and relative performance assessments. The proposed GRPO approach incorporates smart initialization, adaptive exploration, and elite-guided updates tailored to the EDP’s structure. Our method consistently produces high-quality, feasible solutions with faster convergence compared to state-of-the-art metaheuristics and learning-based methods. For instance, in the case of the 15-unit system, GRPO achieved the best cost of USD 32,421.67/h with full constraint satisfaction in just 4.24 s, surpassing many previous solutions. The algorithm also demonstrates excellent scalability, generalizability, and stability across larger-scale systems without requiring parameter retuning. These results highlight GRPO’s potential as a robust and efficient tool for real-time energy scheduling in smart grid environments.

This paper considers the optimal economic dispatch of power generators in a smart electric grid for allocating power between generators to meet load requirements at a minimum total cost. We present a decentralized algorithm where, each generator independently adjusts its power output using only a measurement of the frequency deviation of the grid and minimal information exchange with its neighbors. Existing algorithms assume that frequency deviation is proportional to the load imbalance. In practice this is seldom exactly correct. We assume here that the only thing known about this relationship is that it is an unknown, odd, strictly increasing function. We provide a proof of convergence and simulations verifying the efficacy of the algorithm.

SummaryThis paper studies distributed resource allocation problem for agents with input dead‐zone, which is not considered in the existing work. At first, the primal problem is transformed to an auxiliary problem by using the exact penalty method to deal with local inequality constraints. It is assumed that the explicit expressions of cost functions and local inequality constraints are unknown to agents but the values of the cost and constraint functions can be obtained. Under such a setup, the extremum seeking control is used to estimate the gradient information. Thus, to obtain the optimal allocation, a novel distributed algorithm is designed by the virtue of the extremum seeking control and a dynamic compensating mechanism which is used to handle the effects of the input dead‐zone. Due to a two time‐scale structure of the designed distributed algorithm, the semi‐globally practically asymptotical convergence of all agents' decisions to the optimal allocation is obtained by the singular perturbation technique. Finally, numerical examples of economic dispatch in smart grids are given to verify the effectiveness of our proposed method.

Integrating renewable energy into power grids is seen in increase in recent years since these energy sources are sustainable and clean. However, the integration brings about considerable technical challenges associated with fluctuations and uncertainties of the energy availability whilst maintaining the stability of smart grids. The prediction of renewable energy generation is key to achieve optimal power dispatch in renewable-intensive smart grids. However, uncertain interruption and prediction errors will make an optimal decision more challenging. Model predictive control (MPC) is an effective way to overcome the discrepancies between the prediction and the real-world system through a closed-loop correction over iteration process. This study develops an improved MPC scheme used with a hybrid energy storage system for optimal power dispatch in a smart grid. This hybrid renewable energy system consists of a wind farm, a hydrogen/oxygen storage system and several fuel cells (FCs). In this study, particle swarm optimization (PSO) with a back propagation (BP) artificial neural network is developed to predict the wind energy availability by using measured data. Then, a genetic algorithm (GA) is combined with a state space model (SSM) to achieve the MPC control. A dataset of 24-hour ahead predictive generation is calibrated from the measured data and is defined for optimal power flow between the grid, the wind farm and the storage subsystem so as to balance the supply and load. The optimization target is to achieve a minimal energy exchange between the power grid and the hybrid renewable energy storage system. Based on actual measured data, the test results have shown that the proposed methodology can maximize the local usage of wind power whilst minimizing the power exchange with the grid. An optimal power dispatch strategy is proved to be effective to meet the demand and efficiency with dynamic control of the FCs. The usage of the intermittent wind power is increased from 45% to 90% in the four test studies. Therefore, this work can minimize the impact of fluctuating renewable energy on the power grid and enhance uptakes of FC-based energy systems. This is particularly economic and relevant to the remote and under-developed regions where their power networks are weak and vulnerable.

This paper presents a novel approach to economic dispatch in smart grids equipped with diverse energy devices. This method integrates features including photovoltaic (PV) systems, energy storage coupling, varied energy roles,... | Find, read and cite all the research you need on Tech Science Press

Expandable deep learning for real-time economic generation dispatch and control of three-state energies based future smart grids

Various distributed optimization methods have been developed for solving problems which have simple local constraint sets and whose objective function is the sum of local cost functions of distributed agents in a network. Motivated by emerging applications in smart grid and distributed sparse regression, this paper studies distributed optimization methods for solving general problems which have a coupled global cost function and have inequality constraints. We consider a network scenario where each agent has no global knowledge and can access only its local mapping and constraint functions. To solve this problem in a distributed manner, we propose a consensus-based distributed primal-dual perturbation (PDP) algorithm. In the algorithm, agents employ the average consensus technique to estimate the global cost and constraint functions via exchanging messages with neighbors, and meanwhile use a local primal-dual perturbed subgradient method to approach a global optimum. The proposed PDP method not only can handle smooth inequality constraints but also non-smooth constraints such as some sparsity promoting constraints arising in sparse optimization. We prove that the proposed PDP algorithm converges to an optimal primal-dual solution of the original problem, under standard problem and network assumptions. Numerical results illustrating the performance of the proposed algorithm for a distributed demand response control problem in smart grid are also presented.

This article proposes a novel optimization technique “Mutation based Statistically tracked GWO (MSGWO)” for solving, smart grid economic load dispatch problem which includes the uncertainties associated with the wind power generation, solar power generation and Plug-in electric vehicles (PEVs). Such a model incorporating renewable energy resources (RERs) faces an innovative challenge with the inclusion of PEVs, which might act as sources, loads and energy storages. One of the foremost concerns with such a complex model is to control the charging and/or discharging of these vehicles as per the hourly load demand of the system to such an extent that it can operate with minimum possible stress on the system with reduced overall optimum cost and emission. The extraordinary strength of the proposed optimization technique, which is tested on IEEE 300 bus system, is demonstrated in the results which are superior to those obtained from other optimization techniques: GA, PSO, GWO, Modified GWO and EO.

As the proportion of flexible load resources in smart grids continues to rise, resulting in increasingly complex grid structures, significant changes in grid characteristics, and increased risks to grid operation and control, it will be difficult to intelligently regulate the grid solely by relying on traditional resource regulation methods, and the dispatchable space for traditional resources will become smaller and smaller. To this end, this paper conducts an exploratory investigation on the modeling techniques for flexible loads participation in smart grid dispatching. First, a classification of the flexible loads involved in grid regulation is made. Secondly, according to the flexible load classification, the modeling techniques of different classes of flexible loads are reviewed and studied; then, the flexible load dispatching modes for different operating states and different control tasks, and under different control methods are discussed deeply. Moreover, the technological economics and feasibility of these different flexible load dispatching modes are compared. Finally, an outlook and conclusion are made.

Decentralized algorithms to solve the economic dispatch problem (EDP) in smart grids have been a significant focus within engineering research due to their advantages in scalability, robustness, and flexibility. Its purpose is to optimize the generation power of each generator to jointly achieve the minimal total generation cost on the premise of satisfying the total demand and generation capacity. Recently, the emergence of data security and the requirement for complex computing have led to a resurgence of activity in this area. To address EDP while considering the issues of private security and computation efficiency, we propose a novel privacy-protected decentralized random sleep algorithm over an unbalanced directed network. On the one hand, the proposed algorithm can effectively protect sensitive information by adding conditional noises in the state exchange. On the other hand, it can also promote computation efficiency over an unbalanced directed network by incorporating the random sleep strategy into the decentralized inexact gradient method with the gradient rescaling technique. It is proved that the proposed algorithm is able to achieve the optimal solution of the EDP. Furthermore, we also provide theoretical proof to guarantee the convergence and privacy properties of the proposed algorithm. Finally, two simulation examples of EDP in smart grids are provided to demonstrate the effectiveness of the proposed algorithm.

This paper gives an overview of the Particle Swarm Optimization technique with the aim of investigating its applicability to minimizing losses in a power distribution system. The suitability of this method is investigated by emphasizing the impact of its intrinsic parameters on the results. The investigation employs particle swarm optimization on a test system by controlling the generator voltages, transformer taps and the reactive power in the capacitor banks for each load bus. In total it contains 33 control variables: 5 generators (not including the terminal bus), 4 transformers and 24 capacitor banks. A theoretical approach of the PSO is given in the beginning, followed by the simulation results and analyses.

Increasing penetration of renewable power sources (RESs) is bringing more uncertainties to power systems. Real-time economic dispatch should be able to handle the fluctuations caused by the load as well as RESs, and obtain new optimal operating points after deviating from original generation schedules. This paper proposes a generation adjustment algorithm based on the base point and participation factor method. The objective of the method is to obtain fast adjustments to generators' real power outputs in real-time economic dispatch. The proposed method achieves significant and consistent improvements comparing to the original participation factor method by using a more precise model of transmission losses in the optimization process. The computational burden and execution time of the proposed method is much less than OPF and heuristic economic dispatch methods. The proposed method and its effectiveness are tested using IEEE 30-bus system, IEEE 118-bus system and GuangDong 1018-bus system. Simulation results are demonstrated with comparisons and discussions.